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The aim of the present work is to apply the Caputo-Fabrizio fractional derivative to the heat transformation of a second grade fluid. The flow is analyzed under the effect of magneto hydrodynamic together with heat transfer as well as Darcy’s law. The infinite vertical plate is subjected to a more general time dependent motion. Moreover, on the thermal aspects of the infinite plate, we are taking into account the exponential heat phenomena. Exact analytical solutions are obtained by using Laplace transform method to the set of dimensionless fractional governing equations, containing the momentum and energy equations subjected to the boundary and initial conditions. Solutions are plotted graphically to analyze the effect of different parameters i.e. fractional parameter α, Grashof number and Prandtl number on the physical behavior of the fluid flow and temperature.